There has been a recent trend that Video-on-Demand (VoD) providers such as Netflix are leveraging resources from cloud services for multimedia streaming. In this paper, the authors consider the scenario that a VoD provider can make reservations for bandwidth guarantees from cloud service providers to guarantee the streaming performance in each video channel. They propose a predictive resource auto-scaling system that dynamically books the minimum bandwidth resources from multiple data centers for the VoD provider to match its short-term demand projections. They exploit the anti-correlation between the demands of video channels for statistical multiplexing and for hedging the risk of under-provision.